You must fully disclose and deal with the issue. Failure to disclose can be grounds for denaturalization (assuming you were granted) and removal for misrepresentation. Retain counsel before filing for naturalization.
Voting records are available. Who you may voted for is not. Failure to disclose on the naturalization application may result in denial or revocation of naturalization if detected. There are a few exceptions that may permit you to go forward with naturalization application but you should explore these with an attorney before going forward.
You have a major problem.
You need to retain an experienced immigration lawyer, whether myself or one of my colleagues, to review all the facts, and advise you BEFORE you file anything with USCIS.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.